What is (19ln(y/x+5)-ln(y/x))/5-y/x ?

The solution to (19ln(y/x+5)-ln(y/x))/5-y/x is (ln(((y+5x)^{19})/(yx^{18)}))/5-y/x

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simplify (19ln(y/x+5)-ln(y/x))/5-y/x

simplify

\frac{19 ln ( \frac{y}{x} + 5 ) - ln ( \frac{y}{x} )}{5} - \frac{y}{x}

\frac{ln ( \frac{( y + 5 x ) ^{19}}{y x ^{18}} )}{5} - \frac{y}{x}

Solution steps

\frac{19 ln ( \frac{y}{x} + 5 ) - ln ( \frac{y}{x} )}{5} - \frac{y}{x}

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

19 ln (\frac{y}{x} + 5) = ln ((\frac{y}{x} + 5)^{19})

= \frac{ln ( ( \frac{y}{x} + 5 ) ^{19} ) - ln ( \frac{y}{x} )}{5} - \frac{y}{x}

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((\frac{y}{x} + 5)^{19}) - ln (\frac{y}{x}) = ln (\frac{( \frac{y}{x} + 5 ) ^{19}}{\frac{y}{x}})

= \frac{ln ( \frac{( \frac{y}{x} + 5 ) ^{19}}{\frac{y}{x}} )}{5} - \frac{y}{x}

Simplify

\frac{( \frac{y}{x} + 5 ) ^{19}}{\frac{y}{x}} : \frac{( y + 5 x ) ^{19}}{y x ^{18}}

= \frac{ln ( \frac{( y + 5 x ) ^{19}}{y x ^{18}} )}{5} - \frac{y}{x}

ln (\frac{x}{\frac{x}{2}})

ln (\frac{20474}{375}) \cdot 4

10 lo g_{10} (\frac{\frac{2}{π}}{1 0 ^{- 12}})

\frac{1}{2} ln (x) - ln (x + 1)

2 ln (4) - 2 ln (\frac{1}{2})

What is (19ln(y/x+5)-ln(y/x))/5-y/x ?
The solution to (19ln(y/x+5)-ln(y/x))/5-y/x is (ln(((y+5x)^{19})/(yx^{18)}))/5-y/x